Multiplication of Integers

Always remember the following when multiplying integers:

If both of the integers are positive, then the answer will be positive.

           i.e. (positive)(positive) = POSITIVE

If both of the integers are negative, then the answer will be negative.

           i.e. (negative)(negative) = POSITIVE

If one of the integers is positive and the other integer is negative, then the answer will be negative.

           i.e. (positive)(negative) = NEGATIVE
                            OR
                 (negative)(positive) = NEGATIVE

Multiplying 2 integers

Find the product of the absolute values of the integers.	1. (-8)(7) = ? \|-8\| = 8 and \|7\| = 7 So 8 x 7 = 56 2. (8)(-7) = ? \|8\| = 8 and \|-7\| = 7 So 8 x 7 = 56 3. (-8)(-7) = ? \|-8\| = 8 and \|-7\| = 7 So 8 x 7 = 56 4. (8)(7) = ? \|8\| = 8 and \|7\| = 7 So 8 x 7 = 56
Determine the sign of the answer. (Using rules listed above)	1. (negative)(positive) = NEGATIVE Thus, (-8)(7) = -56 2. (positive)(negative) = NEGATIVE Thus, (8)(-7) = -56 3. (negative)(negative) = POSITIVE Thus, (-8)(-7) = 56 4. (positive)(positive) = POSITIVE Thus, (8)(7) = 56

Multiplying more than 2 integers

Method 1:

Work from left to right, multiplying the integers two at a time. Use the rules above to determine the sign of each answer.

-5 x (-9) x 3 x (-7) x 2 = ?
45     x 3 x (-7) x 2 =
135   x (-7) x 2 =
-945      x 2 =
-1890

Method 2:

Find the product of the absolute values of all the integers. To determine the sign of the answer,
remember the following:
     *If there is an even number of negative factors
        in the problem, then the answer is POSITIVE.
     *If there is an odd number of negative factors
        in the problem, then the answer is NEGATIVE.
     *If there are no negative factors in the problem,
        then, of course, the answer is POSITIVE.

Example 1:

-3 x 4 x (-7) x 5 = ?

There is an even number of negative signs in this problem, so the answer will be POSITIVE.

3 x 4 x 7 x 5 = 420

Thus, -3 x 4 x (-7) x 5 = 420

Example 2:

9 x 3 x (-5) x (-2) x (-8) = ?

There is an odd number of negative signs in
this problem, so the answer will be NEGATIVE.

9 x 3 x 5 x 2 x 8 = 2160

Thus, 9 x 3 x (-5) x (-2) x (-8) = -2160